So you attempt to start Kodi from the Mate desktop, right? Do you get any error output to the console? In case open a terminal emulator and there run:/DietPi/dietpi/misc/start_kodi
Check back console output there, if it fails.

Did you try to choose Kodi as autostart option via dietpi-autostart?
This would work around the doubled xserver start. Not sure if this might be related to the issue.